Edge Detection And Shape Recovery Based On Geometrical Property

In this paper, an image is looked as a function, and the function is used in image disposal and pattern recognition. The process in that the image is generated is the process that the solid is perspectively projected from the three-dimensional space to two-dimensional plane and in the process many factors (for example: the illumination) would affect the image generated. So in the image disposal and in the pattern recognition, the image would be treated as the two-dimension function.The edge detection is the important role in the image disposal. The classical method of the edge detection is built on the grad of the image function, and in this method the edges are detected well, (especially the LOG operator). But in the image the different parts' qualities are different, the edge detection's result is not good when the method of the LOG operator uses one limit. So in this paper the edges are detected and there are different limits in the different parts. The image is divided to different parts by result that the image is analyzed by the variogram function. In the image the edges are detected by the different limits in the different parts whose qualities are different.The data of the image are constructed a surface and a surface builds a function. The method of the grad is based on the function. But it does not reflect the essence of the surface, because the grad is a parameter that is based on one plane. In this paper the essence of the surface is analyzed to get the essence of the image and the method of the edge detection. Because the data mutate on the position that is the edge, the normal curvature on some orientation changes from positive to negative. So it is thought whether some point is judged the edge-point by this character.Because there is the good method of the edge detection, it providesinthe condition for the shape recovery from the contour in an image. In this paper the focus is introduced as a parameter to resolve this problem that is the recovery from an image that is a perspective projection of a cylinder. The method of recovery is built from the principle of the perspective project and the direction of the cylinder's axis is recovered.